Lawrence Berkeley National Laboratory

We study the nuclear magnetic resonance (NMR) spin-lattice relaxation rate 1/T1 in random one-dimensional spin chains as a function of the temperature and disorder strength. In the zero temperature limit, the system displays a disorder-induced quantum phase transition between a critical Tomonaga-Luttinger liquid (TLL) phase and a localized Bose glass phase. The 1/T1 is investigated across this transition using large-scale simulations based on matrix product state techniques. We find that this quantity can detect the transition and probe the value of the dimensionless TLL parameter K. We also compute the NMR relaxation rate distributions for each temperature and disorder strength considered. In particular, we discuss the applicability of the stretched exponential fit to the return-to-equilibrium function to extract the 1/T1 experimentally. The results presented here should provide valuable insights in regards of future NMR experiments in realistic disordered spin compounds.